(9-x^-1)/((3x^-1)-(x^-2))

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Solution for (9-x^-1)/((3x^-1)-(x^-2)) equation:


D( x )

x = 0

3*x^-1-x^-2 = 0

x = 0

x = 0

3*x^-1-x^-2 = 0

3*x^-1-x^-2 = 0

t_1 = x^-1

3*t_1^1-1*t_1^2 = 0

3*t_1-t_1^2 = 0

DELTA = 3^2-(-1*0*4)

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)-3)/(-1*2) or t_1 = (-9^(1/2)-3)/(-1*2)

t_1 = 0 or t_1 = 3

t_1 = 0

x^-1+0 = 0

x^-1 = 0

1*x^-1 = 0 // : 1

x^-1 = 0

x należy do O

t_1 = 3

x^-1-3 = 0

1*x^-1 = 3 // : 1

x^-1 = 3

-1 < 0

1/(x^1) = 3 // * x^1

1 = 3*x^1 // : 3

1/3 = x^1

x = 1/3

x in (-oo:0) U (0:1/3) U (1/3:+oo)

(9-x^-1)/(3*x^-1-x^-2) = 0

3*x^-1-x^-2 = 0

x^-1*(3-x^-1) = 0

-1*x^-1 = -3 // : -1

x^-1 = 3

-1 < 0

1/(x^1) = 3 // * x^1

1 = 3*x^1 // : 3

1/3 = x^1

x = 1/3

x^-1*(x-1/3) = 0

(9-x^-1)/(x^-1*(x-1/3)) = 0

-1*x^-1 = -9 // : -1

x^-1 = 9

-1 < 0

1/(x^1) = 9 // * x^1

1 = 9*x^1 // : 9

1/9 = x^1

x = 1/9

x = 1/9

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